Physics 201 MWF10:20 Fall 2000 (Ford)

Exam IV Chapts. 12-15 in Cutnell and Johnson 4th ed.

Show all your work. Partial credit will be given if earned. Write your answers in the blanks provided.


(16 pts) 1. When a quantity of monatomic ideal gas expands at a constant pressure of 4.0 × 10⁵ Pa, the volume of the gas increases from 2.0 × 10^-3 m³ to
8.0 × 10^-3 m³.

a) What is the change in the internal energy of the gas?

Ans. _________________

b) Does the internal energy of the gas increase or decrease?

Ans. _________________


(14 pts) 2. At T = 40 °C the translational rms speed of the atoms of a monatomic ideal gas is 300 m/s. The number of moles of gas and the pressure are kept constant while the volume of the gas is doubled. After the volume is doubled, what is the translational rms speed of the atoms of the gas? (Note: k = 1.38 × 10^-23 J/K.)

Ans. _________________


(10 pts) 3. A circular hole is drilled in a steel plate. When the plate is at a temperature of 40 °C, the diameter of the hole is 4.000 mm. At what temperature of the plate will the diameter of the hole be 3.996 mm? (Note: The coefficient of linear expansion for steel is 12 × 10^-6 (C°)^-1.)

Ans. ________________


(20 pts) 4. A brass pot sits on an electric stove and holds boiling water at 100 °C. The bottom of the pot is 2.0 mm thick and has a surface area of 0.030 m². To prevent the water from boiling too rapidly, an aluminum plate is placed between the pot and the heating element. The plate is 2.0 mm thick and its area matches that of the bottom of the pot. The bottom surface of the aluminum plate, in contact with the heating element of the stove, has a temperature of 180 °C. (Note: For brass the thermal conductivity is k = 110 J/(s·m·C°) and for aluminum it is k = 240 J/(s·m·C°). For water, L_v = 22.6 × 10⁵ J/kg.)

a) What is the temperature at the junction between the bottom of the pot and the top of the aluminum plate?

Ans.______________

b) What mass of water is converted to steam by the heat conducted from the heating element to the water in 10 minutes?

Ans. ______________


(20 pts) 5. Two moles of a monatoomic ideal gas are taken around the cycle shown in the sketch. The temperature of states A, B, C, and D are: T_A = 200 K, T_B = 400 K, T_C = 200 K, T_D = 100 K.

a) What are U, Q, and W for the process C to D? (You must indicate whether each answer is a positive or a negative value. Process C to D is at constant pressure.)

Ans. Q _____________

W _____________

U _______________

b) What are U, Q, and W for the process D to A? (You must indicate whether each answer is a positive or a negative value. Process D to A is at constant volume.)

Ans. Q _____________

W _____________

U _______________


(20 pts) 6. An ice-making machine operates in a Carnot cycle. It takes heat from water at 0 °C and rejects heat to a room at 24 °C. Suppose that 60 kg of water at 0 °C is converted to ice at 0 °C.

a) How much heat is rejected to the room?

Ans. __________________

b) How much energy must be supplied to the machine, in the form of mechanical work?

Ans. __________________